Several ancestors

Topic: Galton–Watson branching · more questions on this topic
‹ A critical offspring law The variance recurrence ›

Starting from Z_0=r independent ancestors, express the extinction probability in terms of the one-ancestor extinction probability q.

Worked answer (click to show)

Each of the r ancestors starts an independent copy of the one-ancestor process. The whole population dies out only when every copy dies out, which has probability q^r.